concprob {SpatialExtremes}

Pairwise empirical and extremal concurrence probabilities

Description

This function computes the pairwise empirical or the pairwise extremal concurrence probability estimates.

Usage

concprob(data, coord, fitted, n.bins, add = FALSE, xlim = c(0,
max(dist)), ylim = c(min(0, concProb), max(1, concProb)), col = 1:2,
which = "kendall", xlab, ylab, block.size = floor(nrow(data)^(1/3)),
plot = TRUE, compute.std.err = FALSE, ...)

Arguments

data

A matrix representing the data. Each column corresponds to one location.

coord

A matrix that gives the coordinates of each location. Each row corresponds to one location.

fitted

An object of class maxstab - usually the output of the fitmaxstab function. May be missing.

n.bins

The number of bins to be used. If missing, pairwise F-madogram estimates will be computed.

xlim, ylim

A numeric vector of length 2 specifying the x/y coordinate ranges.

col

The colors used for the points and optionnaly the fitted curve.

which

A character string specifying which estimator should be used. Should be one of "emp" (empirical), "boot" (bootstrap version) and "kendall" (kendall based).

xlab, ylab

The labels for the x/y-axis (may be missing).

add

Logical. If TRUE, the plot is added to the current figure; otherwhise (default) a new plot is computed.

block.size

Integer specifying the block size for the empirical and bootstrap estimator.

plot

Logical. If TRUE (default) a plot is produced.

compute.std.err

Logical. If TRUE, standard errors are estimated using a jackknife procedure. It is currently only available for the Kendall estimator.

...

Additional options to be passed to the plot function.

Value

This function returns invisibly a matrix containing the pairwise distances and the concurrence probability estimates.

Author(s)

Mathieu Ribatet

References

Dombry, C., Ribatet, M. and Stoev, S. (2017) Probabilities of concurrent extremes. To appear in JASA

See Also

fmadogram, lmadogram

Examples

n.site <- 25
locations <- matrix(runif(2*n.site, 0, 10), ncol = 2)
colnames(locations) <- c("lon", "lat")

##Simulate a max-stable process - with unit Frechet margins
n.obs <- 100
data <- rmaxstab(n.obs, locations, cov.mod = "whitmat", nugget = 0, range = 1,
smooth = 1.75)

##Compute the F-madogram
concprob(data, locations)

##Compare the F-madogram with a fitted max-stable process
fitted <- fitmaxstab(data, locations, "whitmat", nugget = 0)
concprob(fitted = fitted)